Paul de Boer

Additive Structural Decomposition Analysis and Index Number Theory: An Empirical Application of the Montgomery Decomposition

ABSTRACT In recent years, a large number of empirical articles on structural decomposition analysis, which aims at disentangling an aggregate change in a variable into its r factors, has been published in this journal. Commonly used methods are the average of the two polar decompositions and the average of all r! elementary decompositions (Dietzenbacher and Los, 1998, D&L). We propose to use instead the ‘ideal’ Montgomery decomposition, which means that it satisfies the requirement of factor reversal imposed in index number theory. We prefer it to the methods previously mentioned. The average of the two polar decompositions is not ‘ideal’, so that the outcome depends on the ordering of the factors. The average of all elementary decompositions is ‘ideal’, but requires the computation of an ever increasing number of decompositions when the number of factors increases. Application to the example of D&L (four factors) shows that the three methods yield results that are close to each other.

Price effects in input-output relations : a theoretical and empirical study for the Netherlands, 1949-1967

1. Introduction.- 1.1 Preliminary remarks.- 1.2 Outline of the study.- 2. Theory of production and costs.- 2.1 Introduction.- 2.2. Assumptions underlying neo-classical theory of production and costs.- 2.3. Elasticities of substitution.- 2.4. On the existence of a unique cost minimum.- 2.5. Neo-classical theory of costs.- 2.5.1. General theory.- 2.5.1. Homogeneous production functions.- Appendix 2.A. Proof of theorem 1.- Appendix 2.B. Proof of corrolary 1.- Appendix 2.C. A generalization of lemma 2 of Barten, Kloek and Lempers.- Appendix 2.D. A modified version of proposition 7 of Shephard.- 3. Constant elasticities of substitution class of production functions.- 3.1. Introduction.- 3.2. Neo-classical properties of the CES production function.- 3.3. Application of the theory of costs to the h-homogeneous CES production function.- 3.4. The two-level CES production function.- Appendix 3.A. Theoretical restrictions on the parameters of the two-level CES production function.- Appendix 3.B. Derivation of input demand relations, the cost function, the Allen partial elasticities of substitution for the two-level CES production function and a reformulation for time series analysis.- 4. Theory of price effects in input-output relations: some models.- 4.1. Introduction.- 4.1.1. Traditional input-output analysis.- 4.1.2. Generalized input-output analysis: an overview.- 4.2. Generalization of input-output analysis based on one-level CES production functions.- 4.3. Introduction of technical change into the generalized input-output model.- 4.4. The two-level CES production function in input-output analysis.- 4.5. Aggregation of the demand relations for a firm to a demand relation.- of an industry.- 4.6. Two other studies dealing with substitutability in input-output analysis.- 4.6.1. The approach by Theil and Tilanus (1964).- 4.6.2. The approach by Kreyger (1978).- Appendix 4.A. The CBS classification of sectors.- Appendix 4.B. Constancy of input-output ratios.- 5. Methods of estimating price effects in input-output relations.- 5.1. Introduction.- 5.2. Conceptualization.- 5.3. Estimation of the model.- 5.4. Applying methods of estimation to generalized input-output models.- Appendix 5. A. Maximum likelihood estimation in case of autocorrelation within an input group.- 6. Estimated price effects in input-output relations: the Netherlands, 1949-1967.- 6.1. Introduction.- 6.2. Assembling the data.- 6.3. Performance of one-level CES models, 1949-1958, compared with traditional models.- 6.3.1. Parameter estimates.- 6.3.2. Predictive performance.- 6.4. Application of one-level CES models to 1949-1966.- 6.4.1. General.- 6.4.2. Comparison between methods.- 6.4.3. Comparison between models.- 6.5. Comparison of the estimates between the two periods of observation.- 6.6. Application of the two-level CES model.- 6.6.1. Performance of the two-level CES model, 1949-1958.- 6.6.2. Extension of the period of observation to 1949-1966.- 6.6.3. Comparison of the estimates between the two periods of observation.- 6.7. Summary of the conclusions.- Appendix 6.A. Tables relating to the one-level CES models.- Appendix 6.B. The statistics of Spearman, Theil and Somermeyer.- Appendix 6.C. Tables relating to the two-level CES model.- 7. Summary and conclusions.- Notes.- References.- Authors index.

On the relationship between production functions and input-output analysis with fixed value shares

this paper we examine the necessary and sufficient conditions for constancy of the value input-output coefficients. In his well-known article Klein1 studied the same problem. Nevertheless, there is a striking difference between his approach and ours. Klein assumes that all inputand output prices are known, either as fixed or as given functions of input demand. He subsequently shows that every production function which is zero-homogeneous in all inputs and outputs yields constant value shares of inputs in the outputs, assuming optimal allocation of both. This is true whenever one specific vector of inputand output prices is considered. We, however, derive conditions of invariance of value shares for any exogenously determined variable vector of input prices and output prices. This additional requirement restricts the class of admissible production functions. First, we consider the case of a single homogeneous output per sector. We show that constancy of value input-output coefficients holds good if and only if the production function is of the linear-homogeneous CobbDouglas type. The sufficient condition is well-known, but contrarily to common belief the necessity of the condition has as yet not been established.

Spanish Imports of Manufactures and the European Union: An Empirical Assessment of the Entry

This paper investigates the consequences of Spains accession to the European Union on its imports of manufactures. To that end the realised shares of GDP and the supplies of Spains main trading partners in the transition period 1986–1992 are compared with the shares that are predicted by means of a model that is estimated using data that relate to the pre-integration period.

PREDICTING NEGATIVE EFFECTS OF THE SECOND INTIFADA: AN EX-POST EVALUATION OF SOME MODELS

In 2003, the World Bank (WB), the International Monetary Fund (IMF) and de Boer and Missaglia (DBM) constructed models for the estimation of the 2002 macro-economic indicators of the economy of Palestine. In 2007, IMF and WB provided the consensus estimates of these figures using data that are more up-to-date and more complete than those available in 2003. This note proposes an ex-post evaluation of the predictive performance of the models of WB, DBM and IMF. A comparison of the models of WB and DBM, which are both micro-founded computable general equilibrium models using the same data, reveals that DBM strongly outperforms WB. We argue that the shortening of the time horizon and the quantity adjustment following the dramatic shock explain why our model performs much better. A comparison of DBM with IMF (a simple macro-founded income-expenditure model) also shows that our model performs better.

Structural Models of Factor Demands and Technological Change: An Empirical Assessment of Dynamic Adjustment Specifications for Sectors of the Dutch Economy

In this paper, we combine a translog cost functional form with an adjustment process according to the error correction mechanism to explain the simultaneous determination of factor demands and tech...

Estimated Price Effects in Input-Output Relations: The Netherlands, 1949–1967

This chapter is devoted to an application of the theory presented in the previous chapters to the Dutch economy.

Theory of Production and Costs

The central concept in the theory of production and costs is the production function. It relates quantities of inputs into a production process to the output of that process. The goods and services appearing in a production process are called factors of production; for any quantitative combination of these factors the production function defines the maximal output to be realized. Its main purpose is to show the possibilities of substitution between the factors of production to achieve a given output, assumed to be a single one.

Constant Elasticities of Substitution Class of Production Functions

In their pioneering article Arrow, Chenery, Minhas and Solow (1961) introduced the two-factor C.E.S. production function: